There are two factories located at place P an | vedclass

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(A) Let $x$ and $y$ be the units transported from factory $P$ to depots $A$ and $B$ respectively. Then,$8-x-y$ units are transported from $P$ to $C$.T

Vedclass · Accepted Answer

$1550$

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(A) Let $x$ and $y$ be the units transported from factory $P$ to depots $A$ and $B$ respectively. Then,$8-x-y$ units are transported from $P$ to $C$.The units transported from $Q$ are:To $A$: $5-x$To $B$: $5-y$To $C$: $6-(5-x)-(5-y) = x+y-4$The constraints are:$x \geq 0, y \geq 0$$x \leq 5, y \leq 5$$x+y \leq 8$$x+y \geq 4$The total cost function $Z$ is:$Z = 160x + 100y + 150(8-x-y) + 100(5-x) + 120(5-y) + 100(x+y-4)$$Z = 160x + 100y + 1200 - 150x - 150y + 500 - 100x + 600 - 120y + 100x + 100y - 400$$Z = 10x - 70y + 1900 = 10(x - 7y + 190)$Evaluating $Z$ at corner points of the feasible region:$(0,4): Z = 10(0 - 28 + 190) = 1620$$(0,5): Z = 10(0 - 35 + 190) = 1550$$(3,5): Z = 10(3 - 35 + 190) = 1580$$(5,3): Z = 10(5 - 21 + 190) = 1740$$(5,0): Z = 10(5 - 0 + 190) = 1950$$(4,0): Z = 10(4 - 0 + 190) = 1940$The minimum cost is $1550$ at $(0,5)$.

From/To	$A$	$B$	$C$
$P$	$160$	$100$	$150$
$Q$	$100$	$120$	$100$

	Brand $P$ ($kg$ per bag)	Brand $Q$ ($kg$ per bag)
Nitrogen	$3$	$3.5$
Phosphoric acid	$1$	$2$
Potash	$3$	$1.5$
Chlorine	$1.5$	$2$

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